Problem: Let $f(x) = -9x^{2}+2x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Solution: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-9x^{2}+2x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -9, b = 2, c = 1$ $ x = \dfrac{-2 \pm \sqrt{2^{2} - 4 \cdot -9 \cdot 1}}{2 \cdot -9}$ $ x = \dfrac{-2 \pm \sqrt{40}}{-18}$ $ x = \dfrac{-2 \pm 2\sqrt{10}}{-18}$ $x =\dfrac{-1 \pm \sqrt{10}}{-9}$